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Approximation of functions and their derivatives by analytic maps on certain Banach spaces
Approximation of functions derivatives analytic maps
2010/11/24
Let X be a separable Banach space which admits a separating polynomial; in particular X a separable Hilbert space. Let $f:X \rightarrow R$ be bounded, Lipschitz, and $C^1$ with uniformly continuous d...
Uniform approximation of the integrated density of states for long-range percolation Hamiltonians
the integrated density of states long-range percolation Hamiltonians
2010/11/23
In this paper we study the spectrum of long-range percolation graphs. The underlying geometry is given in terms of a finitely generated amenable group. We prove that the integrated density of states (...
On the power of function values for the approximation problem in various settings
function values the approximation problem various settings
2010/11/22
This is an expository paper on approximating functions from general Hilbert or Banach spaces in the worst case, average case and randomized settings with error measured in the $L_p$ sense. We define ...
Convex Multivariate Approximation by Algebras of Continuous Functions
Convex Multivariate Approximation Algebras Continuous Functions
2010/11/22
We obtain an analog of Shvedov theorem for convex multivariate approximation by algebras of continuous functions.